29.31.16 problem 915

Internal problem ID [5495]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 915
Date solved : Sunday, March 30, 2025 at 08:23:29 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} \left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+4 x^{2}&=0 \end{align*}

✓ Maple. Time used: 0.402 (sec). Leaf size: 46

ode:=(-x^2+1)*diff(y(x),x)^2+2*x*diff(y(x),x)*y(x)+4*x^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -2 \sqrt {-x^{2}+1} \\ y &= 2 \sqrt {-x^{2}+1} \\ y &= -c_{1} +c_{1} x^{2}-\frac {1}{c_{1}} \\ \end{align*}

✓ Mathematica. Time used: 0.343 (sec). Leaf size: 63

ode=(1-x^2) (D[y[x],x])^2+2 x y[x] D[y[x],x]+4 x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {-4 x^2+4+c_1{}^2}{2 c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 \sqrt {1-x^2} \\ y(x)\to 2 \sqrt {1-x^2} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2 + 2*x*y(x)*Derivative(y(x), x) + (1 - x**2)*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out